175.

If in any field of radiation whatever we have an ideal oscillator of the kind assumed above ([sect:135.] Sec. 135), there will take place between it and the radiation falling on it certain mutual actions, for which we shall again assume the validity of the elementary dynamical law introduced in the preceding section. The question is then, how the processes of emission and absorption will take place in the case now under consideration.

In the first place, as regards the emission of radiant energy by the oscillator, this takes place, as before, according to the hypothesis of emission of quanta ([sect:147.] Sec. 147), where the probability quantity $\eta$ again depends on the corresponding spectral intensity $𝖨$ through the relation [eqn:(265)] (265).

On the other hand, the absorption is calculated, exactly as above, from [eqn:(234)] (234), where the vibrations of the oscillator also take place according to the equation [eqn:(233)] (233). In this way, by calculations analogous to those performed in the second chapter of the preceding part, with the difference only that instead of the Fourier's series [eqn:(235)] (235) the Fourier's integral [eqn:(311)] (311) is used, we obtain for the energy absorbed by the oscillator in the time $\tau$ the expression $\frac{\tau }{4L}\int d\mu ({𝖠}_{\mu }\cos 2\pi \mu t+{𝖡}_{\mu }\sin 2\pi \mu t),$ where the constants ${𝖠}_{\mu }$ and ${𝖡}_{\mu }$ denote the mean values expressed in [eqn:(316)] (316), taken for the spectral region in the neighborhood of the natural frequency ${\nu }_0$ of the oscillator. Hence the law of absorption will again be given by equation [eqn:(249)] (249), which now holds also for an intensity of vibration $𝖨$ varying with the time.